A022469 Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x)).

1, 23, 350, 4450, 51231, 554433, 5756260, 58034900, 572630861, 5558653243, 53279890170, 505596134550, 4759287370891, 44506489496453, 413949260130080, 3832708325439400, 35351885537967321, 325028008388124063, 2980145152236043990, 27260474825925725450, 248857740289031716151

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (23,-179,517,-360).

Formula

a(n) = (21*9^(n+3)-32*8^(n+3)+14*5^(n+3)-3)/672. - Yahia Kahloune, May 25 2013

a(0)=1, a(1)=23, a(2)=350, a(3)=4450; for n>3, a(n) = 23*a(n-1) -179*a(n-2) +517*a(n-3) -360*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
LinearRecurrence[{23, -179, 517, -360}, {1, 23, 350, 4450}, 20] (* Harvey P. Dale, Feb 28 2015 *)

Prog

(Magma) I:=[1, 23, 350, 4450]; [n le 4 select I[n] else 23*Self(n-1)-179*Self(n-2)+517*Self(n-3)-360*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x))) \\ G. C. Greubel, Feb 27 2018

Crossrefs

Sequence in context: A268465 A025973 A277833 * A028030 A022454 A142617

Adjacent sequences: A022466 A022467 A022468 * A022470 A022471 A022472

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved